Changes in the variance of a soil property along a transect, a comparison of a non-stationary linear mixed model and a wavelet transform

- Data on soil pH from a 7-km transect over varied parent material was examined.
- A wavelet analysis identified changes in variance at different scales and locations.
- A linear mixed model (LMM) with non-stationary random effects was identified.
- The LMM showed change points, some comparable with those from the wavelet analysis.

The wavelet transform and the linear mixed model with spectral tempering are two methods which have been used to analyse soil data without assumptions of stationarity in the variance. In this paper both methods are compared on a single data set on soil pH where marked changes in parent material are expected to result in non-stationary variability. The two methods both identified the dominant feature of the data, a reduction in the variance of pH over Chalk parent material, and also identified less pronounced effects of other parent material contrasts. However, there were differences between the results which can be attributed to (i) the wavelet transform's analysis on discrete scales, for which local features are resolved with scale-dependent resolution; (ii) differences between the partition of variation into, respectively, smooth or detail components of the wavelet analysis and fixed or random effects of the linear mixed model; (iii) the fact that the identification of changes in the variance is done sequentially for the wavelet transform and simultaneously in the linear mixed model.